Page 274 - Separation process engineering

Chapter 7. Approximate Shortcut Methods for Multicomponent

Distillation

The previous chapters served as an introduction to multicomponent distillation. Matrix methods are
efficient, but they still require a fair amount of time even on a fast computer. In addition, they are
simulation methods and require a known number of stages and a specified feed plate location. Fairly
rapid approximate methods are required for preliminary economic estimates, for recycle calculations
where the distillation is only a small portion of the entire system, for calculations for control systems, and
as a first estimate for more detailed simulation calculations.

In this chapter we first develop the Fenske equation, which allows calculation of multicomponent
separation at total reflux. Then we switch to the Underwood equations, which allow us to calculate the
minimum reflux ratio. To predict the approximate number of equilibrium stages we then use the empirical
Gilliland correlation that relates the actual number of stages to the number of stages at total reflux, the
minimum reflux ratio, and the actual reflux ratio. The feed location can also be approximated from the
empirical correlation.

7.1 Total Reflux: Fenske Equation

Fenske (1932) derived a rigorous solution for binary and multicomponent distillation at total reflux. The
derivation assumes that the stages are equilibrium stages.
Consider the multicomponent distillation column operating at total reflux shown in Figure 7-1, which has
a total condenser and a partial reboiler. For an equilibrium partial reboiler for any two components A and
B,

(7-1)

Figure 7-1. Total reflux column

Equation (7-1) is just the definition of the relative volatility applied to the reboiler. Material balances for
these components around the reboiler are